Why can't I sculpt on a plane when using Subdivision Surface?
Subdivision Surface modifier (or Subsurf) isn't designed to work with sculpting. Subdivisions added with it are accessible for sculpting only once the modifieir's applied. Multiresolution is the one which is designed for that, allowing to edit subdivided surface with sculpt brushes. There doesn't seem to be any real reason to sculpt with Subsurf.